Based on the traditional concave hexagonal honeycomb structure, three kinds of concave hexagonal honeycomb structures were compared. The relative densities of traditional concave hexagonal honeycomb structures and three other classes of concave hexagonal honeycomb structures were derived using the geometric structure. The impact critical velocity of the structures was derived by using the 1-D impact theory. The in-plane impact characteristics and deformation modes of three kinds of similar concave hexagonal honeycomb structures in the concave direction at low, medium, and high velocity were analyzed using the finite element software ABAQUS. The results showed that the honeycomb structure of the cells of the three types undergoes two stages: concave hexagons and parallel quadrilaterals, at low velocity. For this reason, there are two stress platforms in the process of strain. With the increase in the velocity, the joints and middle of some cells form a glue-linked structure due to inertia. No excessive parallelogram structure appears, resulting in the blurring or even disappearance of the second stress platform. Finally, effects of different structural parameters on the plateau stress and energy absorption of structures similar to concave hexagons were obtained during low impact. The results provide a powerful reference for the negative Poisson’s ratio honeycomb structure under multi-directional impact. The effect of a negative Poisson’s ratio was first discovered in nature. The properties are opposite to those of common materials when stretched or compressed. Material with anomalous properties is called an auxetic material. Auxetic materials have excellent shear resistance, impact resistance, fracture resistance, energy absorption, and vibration isolation properties, etc. In 1987, Lakes made polyurethane foams with a negative Poisson’s ratio property , chiral The honeycomb structure is the best topological structure covering the two-dimensional plane. It is a bionic structure. Compared with the common two-dimensional structure, the honeycomb structure has fewer consumables, a high strength-to-weight ratio, a high rigidity-to-weight ratio, high structural stability, good anti-fatigue characteristics, etc. In addition, the honeycomb structure also has an excellent energy absorption capacity , sound aAuxetic materials and honeycomb structures can be well combined. The excellent mechanical properties of negative Poisson’s ratio honeycomb structures can be applied in everyday life. Therefore, negative Poisson ratio honeycomb materials have been extensively researched. Strek et al.  studied In addition, the in-plane dynamic mechanical properties of auxetic honeycomb structures have also been extensively studied. Through experimental and numerical analysis, Günaydın et al.  comparedAt present, a large number of researchers have extensively studied the in-plane characteristics of honeycomb structures with different element types, but the impact direction of the research is relatively singular. Among many negative Poisson’s ratio cell structures, the concave hexagon structure is special, and it will have different deformation modes and mechanical properties when impacted in different directions. Based on the traditional Concave hexagonal structure, we propose two types of similar concave hexagon honeycomb structures with a negative Poisson’s ratio. The relative density and critical velocity of the hexagonal structure are derived, and the dynamic impact response and energy absorption characteristics of each structure are analyzed by finite element simulation. This research reveals the double shape transformation of the concave direction of the similar concave hexagon structure when it is subjected to an in-plane impact. The research also provides basic information for the study of the impact performance of negative Poisson’s ratio honeycomb structures in multiple directions and applications in multiple scenarios.T is the radius of the ring in the cell of TMH, and RL is the radius of the ring in the cell of LMH.The concave hexagon structure is derived from the traditional concave hexagonal structure  . In thisIn the in-plane crushing of the honeycomb structure, the energy absorption characteristics in the deformation process are closely related to the relative density of the honeycomb structure. The relative density can be expressed as the ratio of the cross-sectional area of a single cell to the rectangular area of the cell contour. In The mechanical properties of the honeycomb structure are mainly determined by the stress plateau and the energy absorption when the honeycomb structure is impacted . The strE is the total energy absorbed.The index to evaluate the energy absorption capacity of honeycomb structures can be expressed in terms of specific energy absorption . It reprAccording to the one-dimensional impact wave theory , the expThe expression for the second critical velocity is as follows:Z-axis direction of the honeycomb structure is limited –(4), the relative density of the honeycomb structure composed of the three kinds of cells can be obtained as follows: In In Based on Equation (6), the specific energy absorption curves of TMH, LMH, and SCEH structure cells under different impact velocities are obtained, as shown in In When the concave hexagonal honeycomb structure is impacted in the other direction, the unit cell only shows the concave contraction of the cell wall. However, when the concave direction of the concave hexagonal honeycomb structure is impacted, the unit cell in the honeycomb structure will collapse regularly. Finally, it will form a regular parallelogram structure  When a similar concave hexagon honeycomb structure is subjected to low-velocity impact in the concave direction, the honeycomb structure appears in two shapes. The two shapes are concave hexagonal morphology and parallel quadrilateral morphology. The first stress plateau corresponds to the concave hexagonal shape, and the second stress plateau is marked by the appearance of a parallelogram shape. In addition, TMH and LMH contain a ring structure, and a transient third stress plateau will appear when entering the compaction stage. The multi-platform mechanism improves the impact resistance of the honeycomb structure. It is beneficial to the application of multi-condition impact resistance.t affects the stress of all platforms in the concave direction of the similar hexagonal honeycomb structure and the α mainly affects the second stress plateau.(2) In the analysis of in-plane responses, TMH, LMH, and SCEH have a second stress platform similar to RHH under low-velocity impact. The stress plateau of the similar hexagonal honeycomb structure is higher than that of RHH and the phenomenon indicates that the three kinds of similar concave hexagonal honeycomb structures are better than RHH under low-velocity impact in the concave direction. In the medium velocity impact and high velocity impact, the inertia generated by the impact will end the cell glue phenomenon and the honeycomb structure cannot form a stable second shape. This causes the second stress platform to blur or even disappear. If the stress platform needs to be raised, it can be changed by α or t. The t. The α has little effect on the specific energy absorption of the honeycomb structure in the concave direction.(3) In the analysis of specific energy absorption, under low velocity impact, the specific energy absorption of TMH and LMH is better than that of SCEH on the whole. The specific energy absorption of SCEH and LMH is better than that of TMH under medium and high velocity impact. SCEH will enter the second shape stage earlier than TMH and LMH, so when the strain of the honeycomb structure reaches about 0.5, the specific energy absorption of SCEH will be higher than that of TMH and LMH. If the stress platform needs to be raised, it can be changed by (4) In the analysis of the deformation modes of three kinds of honeycomb structures, the skew of SCEH is larger than TMH and LMH under low-velocity, medium-velocity, and high-velocity impact.


Introduction: The normalized implementation of the centralized volume-based procurement policy for pharmaceuticals is a concerted push for supply-side structural reform of the pharmaceutical industry in China. The impact of the centralized drug procurement policy on pharmaceutical companies' transition from imitation to innovation is investigated to test whether a positive effect occurs in the innovation landscape of the pharmaceutical market. Methods: The double difference method and a series of robustness tests were used based on data from a sample of listed pharmaceutical companies in Shanghai and Shenzhen A-shares between 2015 and 2021. Results: The study found that the centralized drug procurement policy significantly contributed to the increased intensity of innovation input in the Chinese pharmaceutical industry. In terms of regional and firm nature heterogeneity, it was found that firms in the seven provinces belonging to the three economic regions had a better increase in innovation input intensity than other regions. Firms of state-owned nature had a better increase in innovation input intensity than private companies. The mechanism test found a partial mediating effect of nearly 10% for the cost of sales rate on the innovation input intensity of listed companies and a negative mediating effect on corporate operating profit. Discussion: Further research found that the effect of centralized drug procurement policy on the improvement of innovation quality of listed pharmaceutical companies was evident. The innovation development of Chinese pharmaceutical companies no longer focused on the accumulation of innovation quantity. The centralized drug procurement system results from a game and compromises between many stakeholders. It has effectively reduced the burden of drugs on the public and the cost of drug distribution since its introduction. Internationally, the Group Purchasing Organizations (GPOs) in the United States have attracted many medical institutions to join the system, enhancing negotiating power of GPOs, giving it the upper hand in price negotiations with pharmaceutical suppliers . In New However, it is not enough to consider only drug price and distribution costs in promoting centralized drug procurement. There is a potential risk of causing chaos in the pharmaceutical market, affecting business operations, and breaking the industry’s order of competition and development. China’s supply-side structural reform and the centralized drug procurement policy are being promoted in tandem. So it is essential to regulate the order of competition in centralized drug procurement, protect the interests of enterprises, maintain the healthy development of the industry, and achieve a win-win situation for multiple stakeholders. Pharmaceutical companies, as the source of vitality in the pharmaceutical market, are the source of the supply chain of centralized Volume-Based procurement, are significant stakeholders in the supply-side reform of the pharmaceutical market guided by the centralized Volume-Based procurement policy. The study of pharmaceutical companies’ performance, innovative vitality, and development prospects are of great significance to the future evolution of China’s centralized Volume-Based procurement system.This study has important practical and theoretical significance: in terms of practical significance, the starting point of the centralized drug procurement policy was to encourage innovation among enterprises, prompting pharmaceutical companies to realize that innovation is the lifeline and to move from generic drugs to innovative drugs, improved new drugs, and high-quality generics. However, it is also a reality that the share prices of the pharmaceutical sector plummeted during the implementation of the policy, with several pharmaceutical companies losing market share overnight and causing dramatic upheaval in the industry. So, is the centralized Volume-Based drug procurement promoting the transformation of generic innovation in pharmaceutical companies, and is the industry turmoil a “short pain” or a “long pain”? Is there an increase in investment in innovation to achieve generic transformation? What are the mechanisms of impact? Is there heterogeneity of property rights among the selected pharmaceutical companies? Is there regional heterogeneity in the innovation transformation of selected pharmaceutical enterprises? Suppose there is an increase in innovation investment. What is the performance of the innovation strategies and output results of the selected pharmaceutical enterprises, and is there an emphasis on “quality” or “quantity,” or both “quality and quantity”? The study of these questions will integrate more stakeholder needs for the institutional design of the collection policy and provide experience for pharmaceutical companies to choose their innovation strategies. From a theoretical perspective, the existing literature has mainly explored the impact of centralized Volume-Based procurement policies on the risk of drug shortages, supply stability, the actual operation of the platform, hospitals, and patients, as well as the impact on drug prices and procurement volumes, and the selection of varieties. This paper empirically investigates the relationship between the centralized volume-based drug procurement policy and the innovation of pharmaceutical companies from the perspectives of the company nature, the regional economic level and company innovation strategies. This paper enriches the research related to the transformation of pharmaceutical enterprises and the change in the pharmaceutical industry.Domestic and international studies have repeatedly been published on centralized drug procurement policies and corporate innovation. In terms of corporate operating profits, Mo and Zhou et al. postulated that the development of innovative drugs by Chinese companies would increase corporate profits by at least 50%, effectively compensating for the impact of lower profits from generic drugs after centralized Volume-Based procurement . ManiadaIn terms of drug quality, In the gradual implementation of a drug-centralized purchasing policy in China, Chao became concerned about the quality of labeled generic drugs and had difficulty in ensuring clinical effectiveness and safety . Hu arguRegarding internal management, Li and Shen found that after participating in the centralized Volume-Based procurement bidding, Huahai Pharmaceuticals significantly reduced the number of sales staff, reduced sales costs, increased the number of R&D staff, and focused more on R&D innovation . Yang anRegarding industrial concentration and supplier competition, Lu analyzed pilot vs non-pilot cities for centralized Volume-Based drug procurement with a double difference method, found that the medical institutions in the pilot cities met fine their commitments to agree on the amount of drug use, giving the providers the confidence to lower the price in exchange for their sales . Huang aBased on the above theoretical analysis, it can be concluded that the in-depth promotion of centralized volume-based purchasing of drugs in China has caused an increase in the intensity of innovation investment in pharmaceutical companies. By influencing their internal management, drug profits, production processes, technology, capital pooling, market share, competitors, drug quality, and many other aspects. Therefore, this paper proposes the hypothesis:H1The centralized volume-based procurement policy for drugs organized by the State promotes the selected pharmaceutical companies to increase the intensity of their investment in innovation.The advancement of a policy across the country impacts different firms. Scholars such as Yi and Wang argue that enterprises have internal and external heterogeneity. Enterprise heterogeneity is the basis for a better understanding and appreciation of enterprise behavior . From thProperty rights are an inherent attribute of listed companies and significantly impact their business activities. According to Wang and Zhu, a significant proportion of managers of state-owned enterprises have political experience, and management will follow policies closely out of concern for future political performance . On the H2The centralized volume-based procurement policy for drugs has promoted state-owned enterprises to increase investment in innovation more effectively than private enterprises.The ability of pharmaceutical companies to innovate is closely linked to the state of the local economy. Generally speaking, the more economically developed a region is, the more institutional investors there are, the better the entrepreneurial and innovative atmosphere, and the more support it receives. For example, the high number of universities and research institutes belonging to the three major economic zones can provide more excellent local talents. The cities belonging to the three major economic zones are well built and provide convenient transportation routes and postal services. Drug procurement policies promote the upgrading of the pharmaceutical industry, which requires more financial and intellectual support for pharmaceutical companies. Therefore regional heterogeneity is worth studying. Cui and Chen found that the proportion of intangible assets to total assets in China’s Beijing-Tianjin-Hebei region, Yangtze River Delta region, and Pearl River Delta region is higher than the national average proportion, and the proportion of fixed assets to total assets is lower than the national average proportion . They coH3The centralized volume-based procurement policy for drugs has promoted pharmaceutical companies in the three major economic zones to increase their investment in innovation more effectively than those in the non-three major economic zones.ⅰ A sample of ST and *ST companies.It was given that the State Council’s notice agreeing on the centralized Volume-Based drug procurement policy organized by the State and issued to each region was published on 1 January 2019. The first batch of selected results of centralized Volume-Based drug procurement in the alliance regions was also announced in September of that year. Based on the availability of data, the period 2015–2021 was selected for analysis in this paper, using the time of publication of the notification as the node. For the sample companies, the corresponding exclusions were made according to the following criteria:ⅱ A sample of companies with missing data.‘ST and *ST’refers to stocks of domestic listed companies that are subject to special treatment, also known as delisting risk warnings. Due to its possible delisting at any time, this paper does not do research on such companies.ⅲ A sample of “U” companies.The reason for excluding the sample of companies with “missing data” is that empirical research requires operating data. If it is difficult to obtain the operating data of that listed company, then it is impossible to conduct the next step of the study, so it can only be excluded.According to Article 2 of the Notice on Matters Relating to the Trading of Shares and Depositary Receipts on the Technology Venture Exchange issued by the Shanghai Stock Exchange: If an issuer is not yet profitable, its shares or depositary receipts will be marked with a “U”; this special mark will be removed if the issuer achieves profitability for the first time. This study is an empirical study that requires data on operating income, profit, and sales revenue of each company. Therefore, we can only exclude it.China’s centralized drug procurement policies can lead to individual differences between selected and non-selected pharmaceutical firms and differences between pharmaceutical firms before and after the implementation of the policies. The above two types of differences provide room for this paper to conduct quasi-natural experiments using a double difference model to assess the impact of the policy on pharmaceutical firms’ innovation. Listed pharmaceutical companies selected in the first to sixth batches of drug procurement in Shanghai and Shenzhen A-shares are used as the experimental group. Other listed pharmaceutical companies not selected are used as the control group. Treat variables  distinguish between the experimental and control groups, with the experimental group taking a value of 1 and the control group taking a value of 0.The year 2019 was taken as the first year of implementation of the drug procurement policy . The time variable was used to distinguish the time before and after the implementation of the drug procurement policy, with the year after the implementation of the policy taking the value of 1 and the year before the implementation of the policy taking the value of 0. Considering that there are significant differences in the innovation culture and strength of different pharmaceutical companies, and there are also apparent differences in the same pharmaceutical company in different years, this paper refers to Marianne and Zhou and others to construct a two-way fixed effects benchmark model .i,t denotes the intensity of innovation investment by pharmaceutical company i in year t, measured as the ratio of R&D investment to operating revenue in the CSMAR database. The impact effect of China’s centralized drug procurement policy is measured by the interaction term Policyi,t . If the estimated coefficient α1 is significantly positive, it indicates that there is a positive policy effect of the centralized Volume-Based drug procurement policy on the innovation input intensity of listed pharmaceutical companies; if the coefficient α1 is significantly negative, it indicates that there is a negative policy effect of the centralized Volume-Based drug procurement policy on the innovation input intensity of listed pharmaceutical companies; if the coefficient α1 is not significant, it indicates that the impact of the centralized Volume-Based drug procurement policy is insignificant or not effective at the moment.Based on the aforementioned theoretical analysis and research hypothesis H1, in the empirical test, a double-difference benchmark model of the intensity of innovation input of enterprises by China’s centralized volume-based procurement policy for drugs was constructed as follows:1 should theoretically be significant and positive. Xi,t denotes a set of control variables affecting the innovation input intensity of pharmaceutical firm i in year t; μi and λt denote individual firm fixed effects and time fixed effects respectively; α0 and εi,t denote constant terms and random disturbance terms respectively. This paper uses STATA 17.0 software to analyze the data.According to the previous theoretical analysis, drug procurement policy has a positive effect on the innovation performance of listed pharmaceutical companies in China, and αIn this paper, the intensity of innovation investment (Input) is used as the explanatory variable, with a more considerable Input indicating a more significant proportion of R&D investment as a percentage of operating revenue of a pharmaceutical company. It indicates that the pharmaceutical company attaches greater importance to and invests more in innovation; Input data is obtained from the CSMAR Economic and Financial Research Database created by Shenzhen Sigma Data Technology Co.In addition, the quality of innovation output (Newdrug) and quantity of innovation output (Patent) will be used as explanatory variables in subsequent studies. New drug and Patent data come from the Pharmaceutical Intelligence Network (PIN) built by Chongqing Kangzhou Big Data Co Ltd, one of the most authoritative platforms for extensive data services and empowerment in the health industry in China.Meanwhile, control variables were set according to previous studies, which were shrhfd5, ibd, y1001b, size, tobinq, businessyear, sa, executives. control variables were measured in the same way in different double-difference designs. A top and bottom 1% winsorize treatment was applied to some variables. The specific variable names, variable codes, measurements, and data sources for this study are shown in This section examines the impact of China’s centralized drug procurement policy on the share of R&D investment in operating revenue of selected listed pharmaceutical companies based on changes in the intensity of innovation investment. Columns , ZHOU a, and Ma are the In addition to the core explanatory variables, the estimation results of the control variables from column  of TableSince implementing a centralized Volume-Based drug procurement policy is a continuous dynamic adjustment process, it is necessary to consider further the dynamic effect of centralized Volume-Based drug procurement on the innovation development of pharmaceutical enterprises in China. This section draws on the method of Beck et al.  to conduA particularly important assumption for the use of double difference models (DID) is that “parallel trends” are satisfied. Whether using graphs, regressions, or descriptive statistics, it needs to be shown that the experimental and control groups must be comparable before a shock or policy occurs. This is because the performance of the control group is assumed to be the counterfactual of the experimental group. It can be visually reflected that the coefficients of the double interaction terms  before the implementation of the pooling policy in 2019 are not significant, indicating that the trend of change in the treatment and control groups before the implementation of the pooling policy is the same and there is no significant difference. The coefficient of the double interaction term in 2019 after implementation is marginally insignificant. The coefficients of the double interaction terms in subsequent years  are significantly different from zero, indicating that the selected pharmaceutical enterprises in the treatment group have a greater intensity of innovation input than the non-selected pharmaceutical enterprises in the control group. Therefore, the DID model used in this study satisfies the parallel trend assumption and the effect of policy implementation has some persistence.In addition, this section reflects the regression results in column  of TableTo alleviate the problem of sample selection bias, this section refers to the practice of Sun and Ge. Further, it applies the propensity score matching-dual difference (PSM-DID) method  with a 1:2 nearest neighbor matching method without put-back for robustness testing . Selecting the control variable in the same innovation input intensity benchmark regression as the matching variable and setting the caliper to 0.01, applying the Logit method was used for probability estimation. Propensity scores were obtained before and after matching . It can p-values of the policy dummy variables in the random combination case, and the curves show the kernel density distribution of the estimated coefficients, with the horizontal dashed line being the significance level of 0.1 and the vertical dashed line being the true estimate of the double-difference model of 1.775  and the coefficient estimates obtained based on the random sample are also generally smaller than those obtained in the benchmark regression, which further suggests that the results obtained in this paper are robust.To exclude the effects of endogeneity of policy shocks and individual firm heterogeneity on the study findings, this section conducts a placebo test repeated 500 times concerning Ningbo et al. . Figure The previous regression results suggest that the centralized drug procurement policy significantly increases the intensity of innovation investment by the selected pharmaceutical companies. However, it is still unknown how the centralized Volume-Based drug procurement policy affects innovation in pharmaceutical firms in the context of regional and firm property rights. The following section will further explore the mechanism of action within the ‘black box.'The above analysis has verified the impact of the harvesting policy on selected listed pharmaceutical companies at an industry-wide level. However, as China is a developing country with uneven regional development, the effect of policy implementation is often heterogeneous at the regional level. For many years, the Ministry of Commerce of China has published the “Statistical Analysis Report on the Operation of the Pharmaceutical Distribution Industry,” which contains statistics on the regional distribution of sales from multiple perspectives. We have found that the annual sales of the three major economic zones account for around 40%–50% of total national sales, which is relatively stable and has particular research significance. In terms of spatial distribution, the three economic zones are are located in northern China, southern China and eastern China, which can drive the development of each region and of course attract the investment of resources from each region., with developed transportation, high research, and management level, an excellent economic base, and many enterprises.Other regions have a weaker economic base and fewer enterprises than the three economic zones, but they are rich in resources and have great potential for development. In this paper, we further investigate the effects of the state organization’s centralized Volume-Based procurement policy on the innovation investment of regional listed pharmaceutical companies through the double-difference and mediating effect models. As in columns  to Vitr of TableFor the pharmaceutical industry, introducing national policies has a significant impact on enterprises, such as the promotion of GMP and GSP, medical insurance, and the primary drug catalog. This centralized Volume-Based drug procurement is no exception. Although private pharmaceutical companies can voluntarily make strategic adjustments according to their own development goals, combined with the current situation of the company, and freely control the pace of development, it is easy to seize market opportunities in the market.However, in terms of keeping up with national policy acceptance, safeguarding people’s livelihood, and guiding changes in the industry, state-owned pharmaceutical enterprises are more advanced. Secondly, state-owned enterprises have easy access to information on the future direction of policies and the strength of their promotion. Columns  and Mo, of TableThe previous section found that the centralized drug procurement policy significantly promoted the selected pharmaceutical companies to increase their investment in innovation. The increase in innovation investment by the selected pharmaceutical companies may be due to the increase in profits from the increased market share of the selected products. Alternatively, the lack of profits after winning the pooled procurement may encourage companies to increase their R&D efforts in biologics and innovative drugs. Also, it may be due to the increase in innovation investment by reducing the relative sales costs. The views of scholars and experts differ on the above points, but they remain in qualitative research and less in empirical evidence. The impact of internal corporate mechanisms is not yet known, so the sample chosen for this paper is of some relevance. From the perspective of the sales expense ratio, enterprises save money by reducing the sales expense ratio to encourage corporate innovation, increase investment and improve the level of corporate innovation and innovation capacity. In addition, from the perspective of business profits, high profits promote enterprises to have more strength to carry out innovation work, improve the tolerance of innovation risk, and thus obtain high-quality innovation results. Alternatively, centralized Volume-Based drug procurement policy have not yet divided the “pie,” resulting in companies, as one of the main stakeholders, interrupting the national distribution of mature drug sales networks, reducing profits. So, it opted to enter biologics and innovative drugs to increase its bargaining power in the market.To test the above two mechanisms, this paper uses the stepwise regression method with the coefficient product Sobel test to test the mediating effect. The specific model is as follows.1 are significant at the 10% level when the explanatory variable in the model (3) is sale/revenue, indicating that the selected firms save money and encourage innovation by reducing the sales cost rate. From column (2), the coefficient of policy is more significant after controlling for the mediating variable sale/revenue. However, the coefficient of the mediating variable sale/revenue, is not significant. To explore the reason, this paper uses the Sobel test for mediating effect and finds that the p-value is less than 0.01, indicating that the mediating effect holds, and the calculated mediating effect accounts for 8.98% of the total effect, see 1 is significant at the 5% level when the explanatory variable in model (The regression results of model (2) and model (3) are presented in in model  is profiAs mentioned earlier, centralized Volume-Based drug procurement policy have significantly increased the intensity of firms’ innovation inputs. It is worth considering how the increase in innovation inputs has changed firms’ innovation outputs. It is not enough to consider only the relationship between inputs and outputs without considering corporate strategies in the context of centralized Volume-Based drug procurement. In the context of implementing the centralized Volume-Based procurement policy for drugs organized by the state, many large pharmaceutical companies whose ace products did not win the tender have put all their efforts into researching and developing innovative drugs. Their former negative innovation strategy has become more innovation-driven. Some companies are committed to an indirect innovation strategy through inter-company technology mergers or acquisitions to achieve product differentiation and diversification. Some Enterprises have pursued technological innovation strategies, focusing their vision on low price, high quality, and sufficient output of winning drugs, and vigorously developing new technologies and techniques for generic drugs. Therefore, the centralized Volume-Based drug procurement policy has dramatically influenced the choice of innovation strategies of enterprises based on their strength and the surrounding environment.The linkages and performance of firms’ innovation strategies and innovation outputs under the influence of centralized Volume-Based drug procurement policy have also attracted numerous scholars to explore. According to Chen, the development strategies of pharmaceutical firms can be classified as autonomous, integrated, and joint innovation, and the quality of their innovation output often differs . Marisa Then, Chinese-listed pharmaceutical companies participate in centralized drug procurement in the face of the integration and optimization of the national market by the centralized Volume-Based drug procurement policy. Will they choose to lay out high-end generic drugs and strictly control the quality and safety of their products concerning the consistency evaluation standards of generic drugs? Or will they accelerate the development of innovative drugs to improve national and international competitiveness? Or will they take improved new drugs as the main direction of attack, with equal emphasis on risks and expected returns? Alternatively, will they provide stable generics as the main focus, with an innovative expansion path, or seek corporate mergers, technology mergers, and project integration to improve innovation performance in a short period, all of which is unknown? There is a paucity of research involving drug procurement policies’ impact on pharmaceutical companies’ output performance and a lack of empirical studies. Therefore, the following hypotheses are proposed in this paper from an empirical perspective.H4China’s centralized volume-based procurement policy promotes a change in the innovation strategy of selected pharmaceutical companies, emphasizing innovation quality over quantity.H5China’s centralized volume-based procurement policy promotes a change in the innovation strategy of selected pharmaceutical companies, emphasizing innovation quantity over innovation quality.H6China’s centralized volume-based procurement policy promotes a change in the innovation strategy of selected pharmaceutical companies, placing equal emphasis on innovation quality and quantity.The aforementioned theoretical analysis shows that as drug procurement policies are advanced, there will be significant differences in the innovation output of companies. The pharmaceutical industry is unique in that it attaches importance to protecting intellectual property rights and timely information, such as clinical filings, as required by law. We can differentiate and quantify the quality differences in the innovation output of pharmaceutical companies based on specific criteria to obtain the proper level of innovation and thus help address the question of how the national centralized drug procurement policy affects innovation output. However, the question of choosing appropriate output indicators to measure the quality of innovation output after centralized Volume-Based drug procurement is an urgent issue to be addressed.Yang and Wu took the number of invention patent applications by pharmaceutical companies as innovation output from the input-output activities of enterprises . Wang ani,t denotes the quality of innovation output of pharmaceutical firm i in year t, measured by the number of new drug clinical applications filed by pharmaceutical firms. patenti,t denotes the quantity of innovation output of pharmaceutical firm i in year t, measured by the number of invention patents granted to pharmaceutical firms. Models  according to the industry classification of the China Securities Regulatory Commission. Considering China’s centralized Volume-Based Drug Procurement, listed companies engaged in medical services or medical devices are under much less pressure to innovate than those engaged in drug R&D and manufacturing. The study did not distinguish between business scope. Second, the subject of this study is actually the affected listed pharmaceutical companies, and the description of the China’s centralized Volume-Based Drug Procurement itself is relatively few. Finally, Volume-Based drug procurement has been conducted several times. It is difficult to quantify whether there is an impact on the incentive to innovate when a listed company is selected the first time and then loses in the next procurement.


This work studied two sub-problems of the cooperative state estimation and cooperative optimization of tracking paths in multiple unmanned underwater vehicle (multi-UUV) cooperative target tracking. The mathematical model of each component of the multi-UUV cooperative target tracking system was established. According to the target bearing-only information obtained by each unmanned underwater vehicle’s (UUV) detection, the extended Kalman filter algorithm based on interacting with multiple model bearing-only data was used to estimate the target state in a distributed way, and the federal fusion algorithm was used to fuse the estimated results of each UUV. The fused target state was predicted, and, based on the predicted target state, to achieve the persistent tracking of the target, the particle swarm optimization algorithm was used for the online collaborative optimization of the UUV tracking path. The simulation results showed that the multi-UUV distributed fusion filtering algorithm could obtain a better target state estimation effect, and the online path collaborative optimization method based on the prediction of the target state could achieve persistent target tracking. Target tracking is a hot research direction in the field of UUV applications. In the underwater environment, the UUV mainly depends on its own passive sonar to judge the relative orientation information of a target according to the noise radiation of the target . Under tIn reference , a path-In this paper, a distributed target state estimation algorithm based on IMM-EKF is proposed to solve the problem of multi-UUV cooperative target tracking. Each UUV performs target state estimation in a distributed manner and the estimation results of each UUV are fused through a federal fusion structure. A collaborative path optimization method based on particle swarm optimization (PSO) is proposed to solve the problem of UUV tracking path optimization. One-step prediction is performed based on the fusion filtering results, the predicted target state is used as the path optimization input to optimize the UUV tracking path online in real time, and the tracking performance is improved.Firstly, the definition of the multi-UUV cooperative target tracking problem is given as follows:Definition 1.(Multi-UUV cooperative target tracking problem) assumes that there are multiple UUVs and moving targets with limited prior knowledge in the space. Each UUV carries sensors and can detect target information, which requires each UUV to cooperatively complete the target state estimation according to the detection information. According to the target state estimation result and each UUV space constraint, the tracking path is adjusted to complete the target tracking task.Definition 1 can be modeled by mathematical formulation. The first is the mathematical model of fusion estimation:The result of the target state fusion estimation will be used as the basis for multi-UUV tracking path optimization. The tracking optimization problem can be described as:The above mathematical model is understood as follows. The purpose of multi-UUV cooperative target state fusion estimation is, under the condition that the target state According to Definition 1, the multi-UUV cooperative target tracking problem in this paper can be described as follows:First of all, the tracking plane is two-dimensional and the target is mobile. In the process of motion, the target may change its motion mode at any time. The detection method is bearing-only detection. The UUV carries passive sonar, which can detect the relative bearing information of the target. The tracking mode is active tracking, and the UUV will adjust the tracking path online according to the target state fusion estimation results during the tracking process. The requirement of the tracking task is persistent tracking, that is, to keep the target within the detection range of each UUV at all times. The schematic diagram of multi-UUV cooperative target tracking is shown in Assuming that the UUV only moves in a two-dimensional plane, the following dynamic equation can be established for the UUV :(4)u•=FmThe UUV dynamic model describes the relationship between force, torque, and UUV velocity. In order to describe the relationship between the UUV’s velocity and position, and between the bow’s angular velocity and heading, a kinematic model of the UUV is established as follows:Assume that the target only moves in the two-dimensional plane, and its state variable is It is assumed that the UUV carries passive sonar, and the detection mode is bearing-only detection. The detection information does not consider other detection information except the relative azimuth, and the detection plane is in the two-dimensional plane, without considering the depth factor. The detection angle of the UUV’s passive sonar at time Among them, According to the different target states used for UUVs, the tracking optimization approach includes two aspects: an approach based on current target states and an approach based on target prediction states. The tracking optimization approach based on target prediction states is adopted in this paper.In the process of target tracking, if only the target’s current states are considered, there is a great risk of target loss. As shown in According to the above problem, some studies have addressed this predicament through a diverse range of techniques, such as random weighting, Sage windowing, and adaptive factor adjustments ,10. In tThere are three commonly used control structures in multi-UUV cooperative control systems: centralized, distributed, and hybrid . In the At present, the multi-UUV system is not advanced enough to perform tasks completely autonomously without central intervention, so the existence of a central control node is inevitable. At the same time, it is hoped that each UUV has a certain autonomous ability, and can communicate and cooperate equally. Therefore, the hybrid control structure is an ideal control structure applied to multiple UUV systems. Combined with the above closed-loop tracking task process based on predicting the target state, a finite-set distributed solution framework for solving the multi-UUV cooperative target tracking problem is given, as shown in By solving the framework shown in (1)The target state information is exchanged between the UUVs to complete the fusion estimation of the target state;(2)According to the respective position information and target estimation information fusion between the UUVs, the tracking path optimization is completed.The two collaborations between UUVs also reflect the two keyword problems of solving the multi-UUV cooperative target tracking problem, the multi-UUV cooperative target state fusion estimation problem, and the multi-UUV tracking path cooperative optimization problem.In the process of tracking a target, the sonar detects the orientation information of the target. According to the bearing-only detection model of UUV sonar, the observation equation is nonlinear, so the nonlinear filtering method should be used to estimate the target state. Common nonlinear filtering methods are: extended Kalman filter, unscented Kalman filter, and particle filter . ConsideIn the process of target tracking, due to the variable motion of targets, it is often difficult for a single model to match the real motion of a target. The interacting multiple model (IMM) is a good and computationally efficient method for dealing with the model-matching problem of maneuvering target tracking. Reference  applied The choice of fusion structure also has an important impact on the problem of multi-UUV cooperative estimation. There are three commonly used fusion structures: a distributed structure, a centralized structure, and a hierarchical structure . AccordiIn summary, the structure of distributed fusion estimation based on IMM-EKF and federated fusion is shown in When the target state estimation is conducted and the distributed target state estimation method is used, each UUV according to itself detects the target information independently of the target state estimation based on the IMM-EFK algorithm, which is passed through mutual communication between the estimated results and estimated covariance, finally according to their own estimation information and the other UUV estimation information fusion estimation. The specific steps of the IMM-EKF algorithm are as follows.(1)Input interactionWe first calculate the mixing probability from model The mixed-state estimates and mixed covariance estimates for model (2)Extended Kalman filterTaking State prediction:Error covariance prediction:The Jacobian matrix is calculated. Under the bearing-only detection model, the target observation equation is nonlinear, and the Jacobian matrix needs to be solved to linearize the approximation. The Jacobian matrix is solved as follows:(3)Model probability updateCalculate the likelihood function for model (4)Output interactionBased on the model probabilities, the final state estimate and covariance are obtained using the weighted summation of the estimated results for each filter as follows:In order to improve the accuracy of the target state estimation with multi-UUV, this paper adopts the collaborative estimation method of federal fusion. After each UUV completes the state estimation, it transmits the obtained target state and covariance information to all the other UUVs by broadcasting. Each UUV performs the weighted fusion of the received target state information and the target state information obtained via its own estimation according to the corresponding covariance. The specific fusion rules are as follows:Finally, the distributed cooperative target state fusion estimation algorithm based on IMM-EKF can be described as follows:Finally, the distributed cooperative target state fusion estimation algorithm based on IMM-EKF can be described in The goal of the target tracking task is not to lose the target, that is, to keep the target in the detection range of the UUV sensor, and on this premise, to optimize the tracking path of the UUV to achieve the better detection of the target and reduce the target state estimation error. Firstly, according to the task requirements and practical engineering applications, the objective function of the optimization problem, namely, the fitness function of the particle swarm optimization algorithm, can be designed as follows:The fitness function is composed of three parts, and each part is a penalty function. In the process of seeking the optimal solution in line with the optimization objective, the smaller the fitness function value of the particle position, the smaller the penalty value of the position, indicating that the position is better. The detailed description of the three-part penalty function is as follows:(1)Persistent tracking penalty function(2)Path-crossing penalty functionIn the formula, As for the specific judgment method for path crossing, the current position of the UUVs, and the corresponding instruction position of the particle swarm optimization income as a path segment, there are several trackers with several paths according to the quick rejection in mathematical experiments, judging the line segment intersection method to determine whether the paths intersect, and then judging whether the instruction of the particle swarm optimization algorithm is reasonable. The specific path-crossing judgment method process is described as follows:Firstly, the current position of the UUV is taken as the starting point of the path segment and the corresponding instruction position of the UUV is taken as the end point of the path segment. Each path segment is represented by the starting point and the end point. Then, the path segment of the (3)Instruction safety penalty functionIn the formula, Particle swarm optimization (PSO) is a swarm intelligence optimization algorithm based on birds searching for food . The corupdate ω :(36)ω=–(36). Finally, the optimal solution is obtained or the minimum accuracy requirement is achieved through layer-after-layer iteration.The detailed steps of the multi-UUV cooperative target tracking path optimization algorithm based on particle swarm optimization are shown in In this table, In Firstly, given the number of models In order to verify the feasibility of the method, this section combines the algorithms in (1)The total simulation time was 1500 beats and the sampling time was (2)Target setting. The target state variable was set to (3)UUV setting. In the simulation, using three UUVs for target tracking, a PID controller was used to achieve UUV movement control, using a dynamic model for the UUV heading and (4)The settings of the distributed cooperative target state fusion estimation algorithm based on IMM-EKF. Each UUV used the IMM-EKF algorithm to estimate the target state. Additionally, UUVs can be federally fused locally, according to the target information sent by other UUVs and the local target information. Among them, IMM-EKF contained CV and CT models, the initial model probability was The system noise for all three filters was set as follows:(5)The settings of the collaborative optimization algorithm for tracking a path based on particle swarm optimization. The particle swarm size was set to 200 particles, the maximum number of iterations was 1000, the learning factors were Firstly, the current target fusion estimation state was used as the basis for path optimization, and the simulation results were as follows:In the zoom-in position of Then, the above parameters remained the same. Taking the target prediction state as the input basis for path optimization, the prediction time was set to half of the particle swarm optimization time, and the simulation result is shown as follows.According to the analysis of the multi-UUV cooperative target tracking simulation diagram in The distributed cooperative target state fusion estimation algorithm based on IMM-EKF proposed in this paper can estimate target motion state according to bearing-only information well, obtain a smooth estimation result in a target’s straight motion and turning motion, and has a high estimation accuracy. The cooperative path optimization method based on the particle swarm optimization algorithm can obtain the path points that meet the requirements of persistent tracking according to the target fusion estimation results. The optimization function designed in this study not only completed the task requirements of persistent tracking, but also had a beneficial effect on UUV collision avoidance, such as the path-crossing penalty factor and instruction safety penalty factor. The simulation results show that the distributed cooperative target state fusion estimation algorithm based on IMM-EKF and cooperative path optimization method based on particle swarm optimization can ensure that multiple UUVs can track a target without losing it and avoid collisions when the target moves in a uniform straight line or a turning direction.


With the gradual deterioration of the natural environment, a green economy has become a competing goal for all countries. As a trend of green innovation development, the digital economy has become a research hotspot for scientists. In this article, we study the supply chain management of enterprises in green innovation and digital economy development and complete the identification and demand prediction of warehouse goods through the Internet of Things (IoT) and artificial intelligence (AI). As the stuff meets the goods detection and storage, we employ an intelligent method to detect and classify the goods. The demand prediction analysis is carried out based on historical data on goods demand in the enterprise. The absolute error between the prediction result and the actual demand within 1 week is less than 30 goods by the particle swarm optimization-support vector machine (PSO-SVM) method used in this article. First, the goods identification task is completed based on video surveillance data using YOLOv4, and the recognition rate is as high as 98.3%. This article realises enterprises’ intelligent supply chain management through the intelligent identification of goods and the demand forecasting analysis of goods in the warehouse, which provides new ideas for green innovation and digital economy development. Today’s society is developing rapidly based on the rapid consumption of resources and environmental pollution and destruction, and the contradiction between man and nature is deteriorating . As a reThe information shown in In addition, the application of advanced data collection systems allows enterprises to collect and transmit data from almost all processes. Enterprises face exponential data growth, and demand increasingly shows greater volatility and randomness. Businesses are dealing with an exponential increase in data, and demand is becoming more volatile and erratic. Enterprises cannot effectively exploit the vast amounts of supply chain data available, making it difficult for them to adapt rapidly to changes in demand. As a result, they keep inventory levels high to prevent stockouts, which also raises the cost of inventory . PromotiWith the widespread application of IoT and AI, the digital economy has also been developing rapidly. Numerous new technologies and business models have emerged due to the close relationship between the real world and the digital economy. These innovations have altered the process of creating value and given rise to fresh approaches to resolving the tension between traditional economic growth and environmental protection and fulfilling the value demand for the synergistic growth of economic and environmental benefits . The effIn (1) This article builds an inventory goods recognition model based on the YOLOv4 framework and completes the automatic identification of goods in the warehouse.(2) Forecasting inventory demand in an enterprise’s supply chain based on the PSO-SVM method, achieving the goal of planning enterprise strategies.(3) After completing the model construction, this article performs goods identification and demand forecasting for the enterprise’s near-term inventory based on the proposed framework. The results are consistent with the strategic sector budget.Green innovation is pursued by various enterprises as the focus of current economic development, and IoT technology is an essential means to achieve green innovation. Therefore, this article studies the supply chain inventory problem in digital economy development and completes the supply chain management through machine learning technology to improve the efficiency of enterprise operations and realize green innovation. The specific contributions are as follows.The rest of the article is organised as follows: “Related works” introduces the related works for digital economy development and supply chain optimization; “Machine learning-based enterprise demand and inventory cost analysis model construction” presents the methods employed. “Experiment result and analysis” describes the experiment and results from the analysis of the proposed framework, and the practical test for the framework is also given. “Discussion” discusses the result and the notice that should be paid in the development of digital economy. The conclusion is drawn in the “Conclusion”.Most scholars do not have a unified understanding of digital innovation in manufacturing. Most give different explanations based on different perspectives, mainly based on the three levels of the innovation process, the outcome and the integrated study of both. At the level of digital innovation results, The current digital economy is mainly a forward-looking study of technology’s development and application scope based on the above innovation process and results. With the continuous application of IoT, the above ideas are realised through artificial intelligence and other methods. Applying cutting-edge technology to business development can encourage and support the digital economy.Inventory optimization is using inventory control to reduce a company’s inventory costs, which is crucial to reducing the capital tied up in the company by lowering inventory costs. Inventory control involves the issues of when to restock raw materials and goods, determining the restocking amount, and safety stock. Gunasekaran et al. used three different MCDM methods for ABC analysis to determine the appropriate product for each inventory category. They applied it to inventory management at a large automotive company . SitompuIt is clear from the study of supply chain optimization and the growth of the corporate digital economy that various industries are investigating using artificial intelligence (AI) technology throughout the whole cycle of their enterprise operation to increase efficiency. The application of a large amount of data also brings the data economy come into being. Scheduling for the corporate supply chain provides inventory optimization, identifies commodity products while optimizing inventory, and allows the supply chain to play a part in the enterprise’s digital economy. Only accurate scheduling can achieve green development.Convolutional neural network (CNN) is the primary tool for processing image information. The training process of CNN models is learning the relationships between image pixels, which are reflected in the model parameters through convolutional operations. The convolution process of 3D convolutional neural networks is shown in The 3D convolutional neural network’s unique kernel structure can learn temporal and spatial dimensions data. 3D convolutional neural networks can be trained and used immediately using raw video data as the network’s input, removing the requirement to first remove optical flow and video frame data. Inventory management, sensitive to time information, is one application where 3D neural networks are highly successful at detecting content.The YOLO target detection algorithm is a family of efficient single-step target detection algorithms proposed by This version firstly incorporates the cross stage partial network (CSPNet) based on the YOLOv3 backbone network Darknet, which reduces memory consumption. Secondly, YOLOv4 uses the Mish activation function to reduce the computational cost. The expression of the Mishap function is shown in It can be seen that the Mish activation function does not take an utterly truncated value at negative values, it allows the inflow of negative values with relatively small gradients, and the Mish function is unbounded by this feature, avoiding the problem of gradient saturation . At the same time, the curve of this function is smooth and continuous compared with the traditional Relu function, and the derivative is better, which helps to improve the localization effect on the target. Besides, adding the Squeeze-and-Excitation Net (SENet)  to the detc. The optimal way to solve such problems is to complete demand forecasting based on historical data to explore the data patterns (i.e., to select the optimal For enterprise demand, its inventory changes according to specific patterns, and these patterns are related to various factors such as season, economic level, patterns . This ari.e., the introduction of The optimization problem represented by the above two functions is a convex quadratic programming problem. By adding Lagrangian multipliers to each constraint When using the SVM method to complete enterprise demand forecasting based on historical data, we discovered that the SVM method is easily prone to fall into the local optimum, making it challenging to achieve model optimization. For this reason, this article chose the particle swarm method to optimize the model. PSO is a search algorithm with few parameters and is easy to implement, which searches for the optimal solution by iteration. The main steps of its algorithm are as follows :To represent the process of PSO optimization SVM more visually, the algorithm process update is shown in By optimizing the parameters of SVM, we achieve efficient fitting based on historical inventory data from warehouses in the supply chain to complete inventory forecasting.The current application of IoT in warehouse management of the supply chain is mainly video monitoring technology, so this article selects the highest-selling product in this warehouse in the last month for identification. Because of the enormous sales volume of this product, its mobility is fast, which increases the difficulty of model training. In the model construction, the period of the item appearing under the fixed camera during the working period of a week is selected for data annotation to complete the model training. Meanwhile, to accurately illustrate the model’s performance, three indicators, Precision, Recall and F1-score are chosen to evaluate the model.This study uses 30% of the data as the test, and the standard data division approach is chosen for model validation. The experimental results obtained are shown in YOLO, the most widely used method in target detection research, has a significantly higher recognition rate than its predecessor methods. As can be seen in To complete the analysis of the forecasted commodity demand for this year, this article combines historical data from the company’s warehouse management process over the previous 5 years. To achieve intelligent warehouse management, the outcomes of commodity demand forecasting under various methodologies are shown in According to the results shown in According to To test effectiveness of the method proposed in the practical application, practical test experiments were conducted in this article. The test framework is shown in In the actual testing process, we tested the model recognition rate of the used YOLOv4. We selected a warehouse working peak day within the video surveillance data for testing, and the comparison process is shown on the left side of It can be seen that the proposed method recognises higher data than manual counting in this camera view, which is because mental inattention often occurs in the manual counting process, leading to errors in data statistics. Therefore, the YOLO method used in this article is an excellent way to avoid such problems and improve the accuracy of goods recognition.At the same time, this article forecasted the demand for goods in the latest month and compared it with the value set by the company’s strategy department. In the latest month, the actual need for goods was 47 pieces, while the company’s strategy department was forecast. The forecast of the proposed method was 41.2, rounding the data to 41 pieces, and the difference between the two performances was insignificant. However, during the forecasting process, the strategy department researches various information, such as relevant policies and consumption habits, in detail. This process requires a large amount of human and material resources. The proposed PSO-SVM method completes the demand forecast based on historical data, an essential reference for future policy formulation and strategy adjustment in the strategy department.In today’s high-speed development of IoT, the essence of saving labour costs through high-tech means is a green innovation. In this study, AI is utilised to finish the intelligent transformation of inventory management in the supply chain of firms, following the needs of businesses and the law of economic development. YOLO, as a classical target detection algorithm framework, combines the anchor box of Faster R-CNN with the groundbreaking multi-resolution prediction to achieve a swift and accurate detection effect . YOLOv4 Green innovation drives the development of the digital economy, and technical research around how to use and maintain data will become a hot research topic in the coming period. Overall, the digital economy can significantly improve the efficiency of regional green innovation, which is conducive to practising the new development concept, driving the transformation of the economy to green development, and thus achieving high-quality economic development. Therefore, as the global technological revolution progresses, government departments in various regions must enhance the infrastructure for supporting digital technologies by speeding up the development of 5G and other IoT technologies’ digital infrastructure, reducing the gap in digital construction, expanding the reach of digital technologies across regional boundaries, and laying a solid material foundation for the distribution of digital dividends . Second,This article researches the problem of inventory wisdom management in the enterprise supply chain in the context of green innovation and the digital economy. First, it proposes a warehouse goods identification method based on IoT monitoring data which uses YOLOv4 as a framework and achieves a 98.7% identification rate for items under a fixed monitoring perspective. Second, using historical data on goods demand and the PSO-SVM method, it was possible to predict the future state of the goods market for 6 months. This method outperformed others in this regard, giving businesses a fresh idea for how to move forward with developing green innovation and a data economy based on IoT technology. In future research, improving the types of goods identification, enhancing the accuracy of identification, and taking into account more human and other external factors for prediction model building to improve its robustness will be the focus of work.10.7717/peerj-cs.1416/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj-cs.1416/supp-2Supplemental Information 2Click here for additional data file.


Extracting the fault characteristic information of rolling bearings from intense noise disturbance has been a heated research issue. Symplectic geometry mode decomposition (SGMD) has already been adopted for bearing fault diagnosis due to its advantages of no subjective customization of parameters and the ability to reconstruct existing modes. However, SGMD suffers from rapidly decreasing calculation efficiency as the amount of data increases, in addition to invalid symplectic geometry components affecting decomposition accuracy. The regularized composite multiscale fuzzy entropy (RCMFE) operator is constructed to evaluate the complexity of each initial single component and minimize the residual energy. Combined with the partial reconstruction threshold indicator to filter out specific significant initial single components, the raw signal can be decomposed into multiple physically meaningful symplectic geometric mode components. Therefore, the decomposition efficiency and accuracy can be enhanced. Thus, a rolling bearing fault diagnosis method is proposed based on partial reconstruction symplectic geometry mode decomposition (PRSGMD). Both simulated and experimental analysis results show that PRSGMD can improve the speed of SGMD analysis while increasing the decomposition accuracy, thereby augmenting the robustness and effectiveness of the algorithm. Rolling bearings are critical elements of mechanical equipment systems, the failure of which always causes a chain reaction, resulting in the occurrence of machine damage of varying degrees that may lead to collapses or even accidents in severe cases. Therefore, the health status of rolling bearings is directly related to the reliability of mechanical equipment operation ,2,3. TheAmong them, the parametric adaptive signal decomposition method needs to select the basis function according to the characteristics of the signal in advance, then determine the optimal parameters or coefficients of the basis function adaptively to realize the optimal matched signal during decomposition ,15, wherThe non-parametric adaptive signal analysis method can automatically choose the basis function or its parameters according to the characteristics of the signal itself in the process of signal decomposition in order to obtain physically meaningful components. It thus can effectively extract the intrinsic characteristics of mechanical fault vibration signals. Compared with the parametric adaptive signal analysis method, the nonparametric adaptive signal analysis method does not need to construct a complete dictionary library based on the characteristics of the signal in advance, resulting in higher adaptiveness as well as decomposed components with physical significance. This is why it has been popularly adopted for mechanical fault diagnosis. At present, the common non-parametric adaptive signal analysis methods include Hilbert–Huang transform (HHT) , local mCombining with the symplectic geometry theory, Pan et al. proposed the symplectic geometry mode decomposition (SGMD) method , and by The remaining parts are arranged in the following manner. SGMD solves the Hamiltonian matrix eigenvalues by adopting a symplectic geometric similar transform and reconstructs SGCs based on their relevant eigenvectors, thereby denoising the complex signal and performing the adaptive decomposition. SGMD consists of the following three major procedures.Phase space reconstructionSet the original signal time sequence as 2.Symplectic Obtain s geometric initial single componentIn order to construct the Hamiltonian matrix, the autocorrelation analysis is carried out on the trajectory matrix to obtain the covariance symmetry matrix Decomposition of the matrix The transformed coefficient matrix Diagonal averaging is employed to convert the initial single component matrix 3.Single Component ReconstructionGiven that different characteristic information and noise of the signal tend to be distributed at different scales, the initial single component containing noise tends to be of higher complexity, while the initial single component containing fault characteristic information is of inferior complexity. Therefore, the complexity of each initial single component is evaluated and ordered using the CMFE.CMFE utilizes fuzzy entropy to overcome the mutation of the similarity index of the SGC component in the signal. Meanwhile, aiming at the effect on fuzzy entropy calculation due to the shortening of the time sequence in the coarse granulation process, the mean value of the fuzzy entropy of different crude granulation sequences under the same scale factor is used as the fuzzy entropy value under this scale factor. CMFE is calculated as follows:x(n) with At first, for a given signal Next, for each scale factor, the fuzzy entropy of each coarse-grained sequence After transforming the initial single component matrix (1) Set (2) Construct the phase space trajectory matrix Here, (3) Obtain the initial single component matrix (4) Calculate the RCMFE operator of each initial single component.Among them, the scale factor The initial single component matrix (5) Build (6) Merge ε is usually 0.001; if the termination criterion is not satisfied, go back to step (6) and obtain (7) Calculate the iteration termination criterion The PRSGMD is more accurate in signal decomposition compared to other methods. To compare and analyze, the SGMD, Variational Mode Decompositionvmd (VMD), and Ensemble Empirical Mode Decompositioneemd (EEMD) were used. First, construct the following simulated signal A Hilbert transform was applied to IMF and SGC to obtain their instantaneous characteristics, namely, Instantaneous Amplitudeia (IA) and Instantaneous Frequencyif (IF). They were then compared with the IA and IF of Finally, the comprehensive performance of the four methods was further compared using metrics such as energy error , The results of the signal In terms of the accuracy of decomposition, according to the corresponding correlation coefficients in The results of the above simulation analysis show that although the accuracy of the PRSGMD method is slightly lower than the other three methods when the noise intensity is weak, the effectiveness of the VMD and EEMD methods is significantly reduced or even ineffective when the noise intensity is increased. Although the SGMD has specific anti-noise performance, the decomposition performance cannot meet the requirements in the environment of high-intensity noise. The PRSGMD method is suitable for separating signal and noise, achieves a superior decomposition effect under the noise disturbance of different signal-to-noise ratios, and has favorable anti-noise performance. In terms of computational efficiency, although the decomposition time of the PRSGMD method is less than that of the SGMD method, the decomposition time is still higher than that of the VMD and EEMD methods. There is a need to optimize the filter parameters in the PRSGMD method to reduce decomposition time and improve decomposition efficiency.To further explain the excellencies and practicality of the PRSGMD method, it was applied to rolling bearing vibration signals analysis. The bearing failure experimental equipment is given in Using the Envelope Spectrumes (ES) analysis method to diagnose all the data in this dataset, the data were categorized as diagnosable (Y), with an ambiguous diagnosis (A), and completely undiagnosable (U). Therefore, a new signal analysis method can be applied to data that are completely undiagnosable (U) if it is necessary to test their practicality for rolling bearing fault diagnosis. This method can be applicationed to data that are completely undiagnosticable (U) if a good diagnostic result is achieved. The parameters associated with the data are given in 4 in For comparison, five methods are used for fault diagnosis: ES analysis, EEMD decomposition followed by ES analysis, VMD decomposition followed by ES analysis, SGMD decomposition of the raw signal followed by ES analysis, and PRSGMD decomposition followed by ES analysis. The ES of the PRSGMD decomposition results in The decomposition times of the raw vibration signal using the four decomposition methods are recorded in From the above analysis results, the PRSGMD method can effectively diagnose the faults of rolling bearings. Moreover, compared with the direct ES of the raw signal or using EEMD, VMD, and SGMD methods to decompose, followed by the ES, the PRSGMD method can more accurately extract the fault characteristics of rolling bearings from noise signals.The RCMFE operator is constructed to evaluate the validity of each initial single component after reconstruction, and the physically meaningful SGC components can be effectively obtained by constraining the residual energy to be minimal.Compared with the raw SGMD method, PRSGMD only needs to process partthe s of the initial single components that contain significant modes and does not reduce the operational efficiency as the amount of data increases, which can effectively improve the decomposition speed.Simulation and experimental analysis results demonstrate that relative to SGMD, EEMD, and VMD, PRSGMD is advantageous in suppressing endpoint effects and modal confusion, resistance to noise property, and increasing the orthogonality and accuracy of the components, while the overall time consumption of PRSGMD is lower than that of SGMD.Taking aim at SGMD suffersing from a rapid decrease in calculation efficiency as the amount of data increases and the impact of the invalid SGC on the decomposition accuracy during reconstruction, in this paper, the PRSGMD method is proposed for the extraction of rolling bearing fault characteristics information, with the following specific conclusions:It is worth mentioning that the processing of rolling bearing vibration data for variable operating conditions and the convergence of the algorithm in PRSGMD need further exploration.


In this paper, we propose a method that uses the idea of decoupling and unites edge information for semantic segmentation. We build a new dual-stream CNN architecture that fully considers the interaction between the body and the edge of the object, and our method significantly improves the segmentation performance of small objects and object boundaries. The dual-stream CNN architecture mainly consists of a body-stream module and an edge-stream module, which process the feature map of the segmented object into two parts with low coupling: body features and edge features. The body stream warps the image features by learning the flow-field offset, warps the body pixels toward object inner parts, completes the generation of the body features, and enhances the object’s inner consistency. In the generation of edge features, the current state-of-the-art model processes information such as color, shape, and texture under a single network, which will ignore the recognition of important information. Our method separates the edge-processing branch in the network, i.e., the edge stream. The edge stream processes information in parallel with the body stream and effectively eliminates the noise of useless information by introducing a non-edge suppression layer to emphasize the importance of edge information. We validate our method on the large-scale public dataset Cityscapes, and our method greatly improves the segmentation performance of hard-to-segment objects and achieves state-of-the-art result. Notably, the method in this paper can achieve 82.6% mIoU on the Cityscapes with only fine-annotated data. Semantic segmentation is a key technology for scene understanding and analysis in the field of computer vision , which bWe evaluate this on Cityscapes  and our A body-edge dual-stream CNN framework for semantic segmentation tasks is proposed. The framework is able to decouple the semantic feature map into two parts, the body and the edge, and explicitly treats the edge information as a separate processing branch.The body stream uses pixel similarity inside the segmented object. By learning the flow-field offsets to warp each pixel toward object inner parts, the body-stream module produces a consistent feature representation for the body part of the segmented object, increasing the consistency of pixel features inside the body.A non-edge suppression layer is added to the edge stream. The body stream contains higher-level information, and the non-edge suppression layer in the edge stream takes advantage of this feature to suppress the interference of other low-level information so that the edge stream can only process edge information and let the edge information flow in the specified direction.Our contributions are as follows:In recent years, the semantic segmentation technology has rapidly developed and the related research has entered a bottleneck period. Some works start from real-time and self-supervision, all aiming to be able to further improve the segmentation performance of semantic segmentation. In addition, improving the segmentation performance of segmenting difficult objects, such as small objects and the refinement of edge segmentation results, is still a problem worth thinking about. There are currently three main directions to solve this problem.Using edge information to help segmentation: Some works use the idea of multi-task learning by adding an edge-detection task to the network so that the model can use the image edge information to improve the segmentation. For example, Lin G  designedRefinement and correction of segmentation results: Another way to improve the segmentation performance is to refine or correct the coarse segmentation results. The work of  uses conOptimizing the loss function: Some works start from the loss function, the current mainstream cross-entropy loss, and its derived correlation loss function in the training process of semantic segmentation networks, whose optimization goal is the KL scatter of the category distribution in the segmentation results and the category distribution in the real labels so these losses focus on the region rather than the edges. A series of works ,24 propoIn this section, we first introduce the general architecture of our proposed new semantic segmentation method, as shown in F can be decoupled into The semantic feature graph The pixels inside the same object are similar to each other, while the pixels at the edges and outside are more different. The body-stream module in this paper is designed to exploit this property by learning the flow field to aggregate the contextual information inside the segmented object, warp the internal pixels to the same direction, generate more consistent feature representations for pixels inside the object, and improve the internal consistency of the segmented object. The body stream consists of two parts: flow field generation and feature warping.Given a feature map H × W × C, where C denotes the channel size and H × W denotes the spatial resolution, we use WideResNet in the architecture of ResNets as the backbone. After the image goes through the ASPP module, we obtain the initial feature map After we generate the flow field, as shown in The specific use of the proposed differentiable bilinear interpolation mechanism in space is used to linearly interpolate the values of the four neighbors of the point δ, and The edge stream is designed to generate edge features, as shown in Five feature maps are extracted from the input image using WideResnet. We denote these five feature maps as Use 1 × 1 convolution to adjust the The non-edge suppression layer is equivalent to acting as a control switch. The features in the body stream come in, and the non-edge suppression layer generates a weight to filter out the shallow irrelevant boundary information, focusing on the edge information and enhancing the ability to identify the edge information. The edges are supervised by cross-entropy loss to suppress the scores of other information in the process of back-propagation, weakening the non-edge information layer by layer. In summary, edge stream focuses only on edge information, which can better extract edge features and retains much effective boundary information, making the segmentation performance better.We use body features and edge features to guide semantic segmentation using the fusion module ASPP as reconstructed features to produce fine semantic segmentation output, as shown in We jointly supervise three parts, ion loss , which aThe final semantic segmentation image output by the network can be computed to obtain the boundary information, and to make the boundary information more accurate, the final semantic segmentation image is regularized, and here we introduce a dual-task regularizer :(3)ζ=12∇G in Equation (3) is a Gaussian filter. The edge information of the output semantic segmentation image is calculated by Equation (3). For the real semantic labels, the edge information is also calculated using the above equation. In order to keep the consistency between them, Equation (4) uses the absolute value of the difference between the two computed results as the loss, thus making boundary maps output by the model similar to the real labels.The boundary prediction of the edge-stream output should be the same as the boundary of the final semantic segmentation result, so the regularization of both is added as follows:λ4 and λ5 are the two hyperparameters controlling the weights of the regular subweights. η parameter can be calculated as follows.In training, in order to back-propagate through (6), we need to calculate the gradient of (3). Let τ = 1. In the process of backward transmission, we approximate argmax operator with τ softmax:τ are hyperparameters. Operator ∇G∗ can be obtained by Sobel kernel filtering. Since argmax is not a differentiable function, we use Gumbel Softmax . The maxWe will conduct experiments on the Cityscapes dataset, which focuses on the understanding of urban street scenes, including semantic-level annotations applied to the semantic segmentation task, with an image resolution of 1024 × 2048, including 30 target categories such as roads, people, cars, buildings, skies, etc., framing up to 50 video images taken in different seasons and weather conditions. Additionally, the entire dataset contains 5000 images with fine annotations. These 5000 images are divided into three parts; 2975 images are used for training the model, 500 images are used for validating the network, and the remaining 1525 images are used for testing the results. In the experiments of our paper, these 30 categories are generalized into 19 categories, such as cars, people, bicycles, etc.We use the PyTorch  framewor(1)IoU and mIoU are standard evaluation metrics for semantic segmentation, which can effectively assess the performance of model prediction regions and reflect the accuracy of model segmentation.(2)The approach in this paper hopes to obtain better edge-segmentation performance with a finely designed edge-processing module, where we introduce a boundary-accuracy evaluation metric  by calcu(3)When the segmentation object is far away from the camera, the segmentation difficulty increases, and we hope that our model can still maintain high accuracy in segmentation. In order to evaluate the performance of the segmentation model segmenting objects at different distances from the camera, we use a distance-based evaluation method  as folloWe use three different semantic segmentation metrics to evaluate our model:Our experiments are conducted on the validation set of Cityscapes, using the complete uncropped images for computation. The architecture in this paper is experimentally compared to current networks with robust semantic segmentation performance. On mIoU, we achieve a 1.1% improvement, as reflected in As can be seen in As can be seen from We evaluate the effectiveness of each component of our method through ablation experiments. Considering that we are building a completely new architecture, we build the complete model step by step on a benchmark network to observe and analyze the impact of each block and loss supervision on the architecture performance. As can be seen from The above figure shows the visual semantic segmentation results of the DeepLabv3+ network and our method (some objects with significant improvement are circled in the figure for comparison), which validates the significant improvement of our method on the Cityscapes dataset. As can be seen in In this paper, we propose a multi-task learning architecture for semantic segmentation and boundary detection. Semantic features are decoupled into body features and edge features by a designed body-stream module and edge-stream module and they are jointly optimized in a well-designed architecture to guide semantic segmentation. The body stream improves the consistency within the segmented objects by learning flow-field offsets that warp the pixels toward object inner parts. The edge stream is an independent edge-processing module that introduces a non-edge suppression layer to make better use of edge information and thus refine the effect of boundary segmentation. The final features are obtained by fusing the body features and edge features using the ASPP module. During the training process, we use relaxation training and a dual task regularizer to produce better segmentation predictions and the fused features are supervised as a result of feature reconstruction by common cross-entropy loss. Our experimental results show that the method has good generality and can significantly improve the segmentation performance for thinner and smaller objects. On the challenging Cityscapes dataset, our method achieves state-of-the-art results with significant improvements on strong baselines.